Functional Performance Analysis of Ball Milling

Excerpts from: Industrial Validation of the Functional Performance Equation for Ball Milling: A Breakthrough Tool for Improving Plant Grinding Performance, to be presented by Robert E. McIvor, Chief Engineer, Grinding Systems, to the 2005 Canadian Mineral Processor’s Conference in Ottawa, Canada, and the 2005 Society for Mining, Metallurgy and Exploration, Inc. Conference in Salt Lake City, USA.

Abstract: The Functional Performance Equation for Ball Milling was first presented in 1988. It has now been used successfully in more than a dozen mineral processing plants. This powerful, yet simple tool provides a new level of understanding of closed circuit grinding. It shows how grinding circuit efficiency is in reality comprised of two distinct and active efficiencies. It demonstrates how circuit production rate is related, collectively, to these two efficiencies, mill energy input, and the grindability of the ore. It provides the means to link circuit performance to plant design and operating variables that can be manipulated, and thus creates an effective strategy for making circuit improvements. This paper covers the derivation and industrial validation of this equation. As part of an engineering and management system that also incorporates suitable measurements and control, other operators can now use this tool to manage the processing performance of their grinding operations with clarity and confidence.

Summary Derivation: Ball mill circuit “classification system efficiency” (or “CSEff”) is defined as the percentage of “coarse” material, versus “fines” in the ball mill. The “effective mill power” (or “EMP”) is the percentage of total mill power (“TMP”) delivered to the “coarse” ore.

Eq.1	EMP = TMP x CSEff
The production rate of “fines” or new product (“PRNP”) by the circuit equals the specific grinding rate of “coarse” material (“SGRC”) per unit of energy applied to it.
Eq.2	PRNP = EMP x SGRC
Substituting:
Eq.3	PRNP = TMP x CSEff x SGRC
Next, divide and multiply the last term of Equation 3 by the lab grindability.
Eq.4	PRNP = TMP x CSEff x SGRC/LabGr x LabGr
The ratio of the plant ball mill grinding rate to the lab mill grinding rate is the relative “ball mill grinding efficiency”(or BMGEff “).
Eq.5	SGRC/LabGr = BMGEff
Substituting yields the Functional Performance Equation:
Eq.6	PRNP = TMP x CSEff x LabGr x BMGEff

The Functional Performance Equation therefore reads as follows:

Each of these is measured during an initial circuit audit. Circuit efficiencies are benchmarked, and changes then made to circuit design and/or operating variables to increase either or both efficiencies. Follow up surveys verify improvements. The full paper text provides a number of industrial plant examples.

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